Using Ibbotson Associates Cost of Capital Data
47. Peer group betas are calculated by taking the sales-weighted average of the betas for each industry in which a company has sales.
25% x 0.60 + 14.75% x 1.10 + 60%. x 0.70 + 0.25% x 0.40 = 0.73 Or using a tabular form:
% Sales in industry Industries OLS beta Peer group betas
25.00% 0.60 0.15
14.75% 1.10 0.1623
60.00% 0.70 0.42
0.25% 0.40 0.001...
Peer group beta 0.7333
48. Using the Vasicek Shrinkage Technique and formula:
Ibbotson (adjusted) beta - (1 - weight) x peer group beta + weight x company beta lbbotson (adjusted) beta = (I 0.20) x 1.25 + 0.20 x 1.75 = 1 + 0.35 = 1.35
49. The industry7 risk premium methodology uses the following equation:
Tn our case, IRPXTZ = (0.90 x 7.8%) - 7.8% = 7.02% - 7.8% = -0.78%
In this case, because the industry7 risk premium is negative, we conclude that is less risky than the market.
50. The easiest way to convert an after-Las capitalization rate to a pretax basis is to divide the after-tax capitalization rate by (1 minus the tax rate).
_ . ,. „ „ ,„rrv After-tax capitalization rate of Company XYZ
Pretax capitalization rate ot Company XYZ =----------------------------------- - --------
1 - tax rate
Pretax capitalization rate of Company XYZ =---- =------ = 23%
1-35% 65%
This process, although not completely accurate, will bring the capitalization rate to an estimated pretax basis.
'1, Small Composite, To determine whether Company XYZ is comparable to the small companies in SIC code 275, we compare the sales and total capital of our company to the sales and total capital of the three smallest companies in the industry7 reported at the top of the paae under Sales and Total.
Tn our case, $10 million and $8 million are below the averages of the figures for the three smallest companies in SIC code 275, so the Small Composite statistics are a good fit for our company.
52. The cost of equity and WACC estimates are presented at tlie bottom of Exhibit 13.3. Since we have already established that Company XYZ is a small company, we are going to look at the "Small Composite" row of that section:
Cost of Equity Capital %
CAPM + size Fama-Frencb CAPM premium three-factor DCF 1-stage DCF 3-stage
Small Composite 10.16 12.78 14.56 11.63 6.50
Also, because we are valuing a very small company, CAPM, adjusted for size and tlie Fama-Frencb three-factor model, will provide a higher, more realistic cost of equity value. So we are looking at:
Cost of Equity Capital %
CAPM + size premium Fama-French three-factor
Small Composite 12.78 14.56
The analyst will exercise further judgment to apply these Small Composite estimates to Company XYZ.
53. The WACC formula is:
WACC= Weke+ Wdkd(l-f)
Where:
Wd and We ~ Market value weights for debt and equity
Because XYZ, as a private company, does not have a market for its securities, one way to apply the WACC is to use the industry-average capital structure as reported in Exhibit 13.3,
The data reported in the "Capital Structure Ratio (%)" section of Exhibit 13.3 allow the analyst to use an industry capital structure in determining the cost of capital for a company without, market data.
Using tlie five-year average debt/total capital ratio for the Small Composite for SIC code 275, we find that the percentage of debt is 43.68% and the percentage of equity is 100 -43.68% ~ 56.32%. With all the data available, we can estimate the WACC for Company XYZ:
WACCXYZ = 56.32% x 20% + 43.68% x 10% = 11.2640% + 4.3680% = 15.63% or 0.1563
54. Using the Small Composite price/sales ratio for the last, five years of 0.59 and the sales for
Company XYZ of $10 million, we WTite:
p
- - = 0.59 Sales
Sales XYZ = SI0,000,000
$10,000,000 P = $5,900,000
Based on the price/sales ratio for SIC code 275, we estimated a market capitalization equivalent of $5.9 million for Company XYZ.
55. The formula for the cost o( equity for Company XYZ using CAPM is:
E (Rj^z) = Rf + Bxyz x (RPJ
XYZ is a private company that does not have market data and therefore does not have a beta. For these situations, the industry beta can be used in absence of the company's own beta. Exhibit 13,3 presents levered, raw, and adjusted betas as well as unlevered betas. If we assume that Company X Y Z has a capital structure comparable to that of the industry average, we can use the adjusted levered beta for Small Composite group of 0.59:
E (Rxyz) = 5.6% + 0.59 x 7.8% = 10.20%
56. BTr = B„ x [1 + debt/equity (1 - t)]
= 0.26x[l + 1.25(1-40%)] = 0.26x[l +0.75]
= 0.26x1.75 = 0.455
57. E (Roclel) = Rf + Bccul x RPm
From Exhibit 13.4, levered raw beta = 0.44, and levered Ibbotson beta - 0.46.
E (Rocid) = 5.6% + (0.44 x 7.8%) = 9.03% E (R^) = 5.6% + (0.46 x 7.8%) = 9.1.8%
58. Adjusted (Ibbotson) beta = (1 - weight) x peer group beta + weight x company beta
Substituting numbers:
0.46 = (1 - weight) x 0.66 + (weight x 0.44) 0.46 = 0.66 0.66 weight + 0.44 weight 0.46 = 0.66 - 0.022 weight 0.22 weight = 0.20 weight = 0.20/0.22 = 0.91
Because the weight assigned to the company beta is quite high, we can conclude that the company beta estimate had a low7 standard error and high statistical significance.
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Using Ibbotson Associates Cost of Capital Data